I did a quick google search, found an interesting article.... snip: Mandated AA Meetings for Atheists
One of the most controversial problems for atheists is court mandated attendance at Alcoholics Anonymous. Insisting that atheists participate in this group could be viewed as promoting a religious belief and therefore an infringement of their rights. This view was supported by a ruling by the US Supreme Court when it was ruled wrong for a judge to have coerced an atheist into attending AA.
I didn't find any groups, but there are other options such as Rational Recovery...I typed into google: atheist alcoholic anonymous in texas -- hopeyfully you can find more info that will be of help.
I had trouble with the family support group, Al-Anon, because it placed the burden of support on a higher power instead of preparing me to take full responsibility for my own healing. I would guess that Atheist alcohol support groups exist for those afflicted and their families.
I especially like what Chris suggested, seeking legal help to get assistance in your situation.
I wish you success in your search for alternatives to Alcoholics Anonymous. There should be a growing number of people seeking such help and the information you find would be valuable to readers of Atheist Nexus.